A332512 Numbers k such that phi(k) == 0 (mod 12), where phi is the Euler totient function (A000010).

13, 21, 26, 28, 35, 36, 37, 39, 42, 45, 52, 56, 57, 61, 63, 65, 70, 72, 73, 74, 76, 77, 78, 84, 90, 91, 93, 95, 97, 99, 104, 105, 108, 109, 111, 112, 114, 117, 119, 122, 124, 126, 129, 130, 133, 135, 140, 143, 144, 146, 147, 148, 152, 153, 154, 155, 156, 157, 161

Offset

1,1

Comments

Dence and Pomerance showed that the asymptotic number of the terms below x is ~ x.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Thomas Dence and Carl Pomerance, Euler's function in residue classes, in: K. Alladi, P. D. T. A. Elliott, A. Granville and G. Tenenbaum (eds.), Analytic and Elementary Number Theory, Developments in Mathematics, Vol. 1, Springer, Boston, MA, 1998, pp. 7-20, alternative link.

Example

13 is a term since phi(13) = 12 == 0 (mod 12).

Mathematica

Select[Range[200], Divisible[EulerPhi[#], 12] &]

Prog

(Magma) [k:k in [1..170]| EulerPhi(k) mod 12 eq 0]; // Marius A. Burtea, Feb 14 2020

Crossrefs

Cf. A000010, A008594, A332511, A332513, A332514, A332515, A332516.

Sequence in context: A260747 A032693 A049745 * A304006 A304948 A087683

Adjacent sequences: A332509 A332510 A332511 * A332513 A332514 A332515

Keyword

nonn

Author

Amiram Eldar, Feb 14 2020

Status

approved